Problem: A circle has a circumference of $20\pi$. It has an arc of length $\dfrac{2}{3}\pi$. What is the central angle of the arc, in degrees? ${20\pi}$ ${12^\circ}$ $\color{#DF0030}{\dfrac{2}{3}\pi}$
Answer: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360 ^ \circ} = \dfrac{s}{c}$ $\dfrac{\theta}{360 ^ \circ} = \dfrac{2}{3}\pi \div 20\pi$ $\dfrac{\theta}{360 ^ \circ} = \dfrac{1}{30}$ $\theta = \dfrac{1}{30} \times 360 ^ \circ$ $\theta = 12^\circ$